New A hybrid Hestenes-Stiefel and Dai-Yuan conjugate gradient algorithms for unconstrained optimization
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Abstract
In this Research we developed a New Hybrid method of conjugate gradient type, this Method depends basically on combining Hestenes-Stiefel and Dai-Yuan algorithms by using spectral direction conjugate algorithm, which is developed by Yang Z & Kairong W [19]. The developed method becomes converged by assuming some hypothesis. The numerical results show the efficiency of the developed method for solving test Unconstrained Nonlinear Optimization problems.
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References
1] خضر, حميد محمد صادق "خوارزميات مطورة للتدرج المترافق
في حل مسائل التصغيرية غير المقيدة" رسالة ماجستير, كلية علوم
الحاسوب والرياضيات جامعة الموصل 2013 .
[2] Abbas Y. Al-Bayati, Abdul-Ghafoor J. and Khalil A. (2009) "Two- Version of conjugate gradient algorithm Based on conjugacy Conditions for unconstrained optimization". American J. of Economics and Business Administration 1, (2).
[3] Al-Baali M. (1985) "Descent property and global convergence of the Fletcher and Revees Method with inexact line search". SIAM J. Numer. Anal 5.
[4] Andrei, N. (2010) "Accelerated scaled memory less BFGS preconditioned conjugate Gradient algorithm for unconstrained optimization" European J. Of Operational Research. 204.
[5] Andrei, N. (2008) "40 conjugate gradient algorithm for unconstrained Optimization" ICI. Technical Report No. 13108.
[6] Andrei N. (2008), "An Unconstrained Optimization test function collection". Adv. Model. Optimization. 10. pp.147-161.
[7] Dai, Y. and Yuan, Y. (1999) "A Nonlinear conjugate gradient method with a strong global convergence property". SIAM J. Optim.,10.
[8] Dai Y. (2001) "New properties of anon-linear conjugate gradient method" Numer. Math. 89.
[9] Dai,Y. and Liao, L. (2001) "New conjugacy conditions and related non-linear CG methods" Appl. Math optim.,(43). Spring-verlag, New York.
[10] Dolan. E. D and Mor´e. J. J, "Benchmarking optimization software with performance profiles", Math. Programming, 91 (2002), pp. 201-213.
[11] Hager, W. and Zhang, H. (2006) "A survey of non-linear conjugate gradient methods" Pacific Journal of Op., 2.
[12] Khalil A. (2008) "New CG method for large-scale unconstrained optimization based on Nazareth theorem". Iraq J. of Statistical science, (13).
[13] Fletcher R. and Reeves G. (1964) "Function minimization by conjugate gradients" computer. Journal, Vol.(7).
[14] Tomizuka. H and Yabe. H, (2004). "A Hybrid Conjugate Gradient method for unconstrained Optimization".
[15] Powell, M. (1984),"Nonconvex minimization calculation and the conjugate gradient method", Numerical Analysis, Lecture Notes in Math., Vol. 1066, pp. 122-141.
[16] Pytlak R. (2009) "Conjugate Gradient Algorithms in Non-convex Optimization" Non-convex Optimization and It's Applications. V. 89, Springer-V.
[17] Touati-Ahmed, D. and Storey, C., (1990), "Efficient Hybrid Conjugate Gradient Techniques". Journal of Optimization Theory and Application (64), 379–397.
[18] Wolfe, M. (1978)."Numerical Methods For Unconstrained Optimization An Introduction". New York: Van Nostraned Reinhold
[19] Yang Z and Kairong W. (2012) ''Anew general form of conjugate gradient methods with guaranteed descent and strong global convergence properties'' Numer Algor 60.
[20] Zoutendijk, G. (1970) "Nonlinear programming, computational methods" In Integer and Nonlinear Programming, J. Abadie(Ed), North- Holand.